Automatic investing is a common feature with mutual fund and ETF IRA accounts. It’s less common with taxable accounts, though its always worth asking if it’s available. Mutual fund companies that have been known to do this include Dreyfus, Transamerica, and T. Rowe Price.
An automatic investing arrangement is particularly convenient if you can do it through payroll savings. You can typically set up an automatic deposit situation through your payroll, in much the same way that you do with an employer-sponsored retirement plan. Just ask your human resources department how to set it up.